Problem: Recently Duff has been a soldier in the army. Malek is her commander.

Their country, Andarz Gu has n cities (numbered from 1 to n) and n - 1 bidirectional roads. Each road connects two different cities. There exist a unique path between any two cities.

There are also m people living in Andarz Gu (numbered from 1 to m). Each person has and ID number. ID number of i - th person is i and he/she lives in city number ci. Note that there may be more than one person in a city, also there may be no people living in the city.

<image>

Malek loves to order. That's why he asks Duff to answer to q queries. In each query, he gives her numbers v, u and a.

To answer a query:

Assume there are x people living in the cities lying on the path from city v to city u. Assume these people's IDs are p1, p2, ..., px in increasing order. 

If k = min(x, a), then Duff should tell Malek numbers k, p1, p2, ..., pk in this order. In the other words, Malek wants to know a minimums on that path (or less, if there are less than a people).

Duff is very busy at the moment, so she asked you to help her and answer the queries.

Input

The first line of input contains three integers, n, m and q (1 ≤ n, m, q ≤ 105).

The next n - 1 lines contain the roads. Each line contains two integers v and u, endpoints of a road (1 ≤ v, u ≤ n, v ≠ u).

Next line contains m integers c1, c2, ..., cm separated by spaces (1 ≤ ci ≤ n for each 1 ≤ i ≤ m).

Next q lines contain the queries. Each of them contains three integers, v, u and a (1 ≤ v, u ≤ n and 1 ≤ a ≤ 10).

Output

For each query, print numbers k, p1, p2, ..., pk separated by spaces in one line.

Examples

Input

5 4 5
1 3
1 2
1 4
4 5
2 1 4 3
4 5 6
1 5 2
5 5 10
2 3 3
5 3 1


Output

1 3
2 2 3
0
3 1 2 4
1 2

Note

Graph of Andarz Gu in the sample case is as follows (ID of people in each city are written next to them):

<image>

Solution (in JAVA):

Solution:
import java.io.BufferedReader;
import java.io.BufferedWriter;
import java.io.FileReader;
import java.io.FileWriter;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.OutputStreamWriter;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.StringTokenizer;

public class C {

    static StringTokenizer st;
    static BufferedReader in;
    static PrintWriter pw;
    static ArrayList<Integer>[]ages, values;
    static int[][]up;
    static ArrayList<Integer>[][]up_min;
    static int[]tin, tout, d;
    static int timer;
    
    public static void main(String[] args) throws IOException{
        in = new BufferedReader(new InputStreamReader(System.in));
        pw = new PrintWriter(new BufferedWriter(new OutputStreamWriter(System.out)));
        int n = nextInt();
        int m = nextInt();
        int q = nextInt();
        ages = new ArrayList[n+1];
        values = new ArrayList[n+1];
        for (int i = 1; i <= n; i++) {
            ages[i] = new ArrayList<Integer>();
            values[i] = new ArrayList<Integer>();
        }
        up_min = new ArrayList[n+1][18];
        for (int i = 1; i <= n; i++) {
            for (int j = 0; j < 18; j++) {
                up_min[i][j] = new ArrayList<Integer>();
            }
        }
        d = new int[n+1];
        for (int i = 1; i < n; i++) {
            int v1 = nextInt();
            int v2 = nextInt();
            ages[v1].add(v2);
            ages[v2].add(v1);
        }
        for (int i = 1; i <= m; i++) {
            int x = nextInt();
            values[x].add(i);
        }
        for (int i = 1; i <= n; i++) {
            Collections.sort(values[i]);
        }
        up = new int[n+1][18];
        for (int i = 1; i <= n; i++) {
            Arrays.fill(up[i], 1);
        }
        tin = new int[n+1];
        tout = new int[n+1];
        dfs(1, 0);
        while (q-->0) {
            int v1 = nextInt();
            int v2 = nextInt();
            ArrayList<Integer> res = new ArrayList<Integer>();
            if (v1==v2) {
                res = values[v1];
            }
            else if (upper(v1, v2)) {
                res = calc(v2, d[v2]-d[v1]);
                res = merge(res, values[v1]);
            }
            else if (upper(v2, v1)) { 
                res = calc(v1, d[v1]-d[v2]);
                res = merge(res, values[v2]);
            }
            else {
                int lca = lca(v1, v2);
                res = calc(v1, d[v1]-d[lca]);
                res = merge(res, calc(v2, d[v2]-d[lca]));
                res = merge(res, values[lca]);
            }
            int a = nextInt();
            int cnt = Math.min(a, res.size());
            pw.print(cnt+" ");
            for (int i = 0; i < cnt; i++) {
                pw.print(res.get(i)+" ");
            }
            pw.println();
        }
        pw.close();
    }
    private static ArrayList<Integer> calc(int a, int k) {
        ArrayList<Integer> res = new ArrayList<Integer>();
        for (int i = 17; i >= 0; i--) {
            if ((1 << i) < k) {
                res = merge(res, up_min[a][i]);
                k -= (1 << i);
                a = up[a][i];
            }
        }
        res = merge(res, up_min[a][0]);
        return res;
    }
    private static int lca(int a, int b) {
        if (upper(a, b))
            return a;
        if (upper(b, a))
            return b;
        for (int i = 17; i >= 0; i--) {
            if (!upper(up[a][i], b))
                a = up[a][i];
        }
        return up[a][0];
    }
    private static boolean upper(int a, int b) {
        return tin[a] <= tin[b] && tout[a] >= tout[b];
    }
    private static void dfs(int v, int p) {
        tin[v] = timer++;
        if (p != 0) {
            up[v][0] = p;
            for (int i = 0; i < Math.min(10, values[v].size()); i++) {
                up_min[v][0].add(values[v].get(i));
            }
            for (int i = 1; i <= 17; i++) {
                up[v][i] = up[up[v][i-1]][i-1];
                up_min[v][i] = merge(up_min[v][i-1], up_min[up[v][i-1]][i-1]);
            }
        }
        for (int to : ages[v]) {
            if (to==p)
                continue;
            d[to] = d[v] + 1;
            dfs(to, v);
        }
        tout[v] = timer++;
    }
    private static ArrayList<Integer> merge(ArrayList<Integer> a,
            ArrayList<Integer> b) {
        ArrayList<Integer> c = new ArrayList<Integer>();
        int s1 = a.size(), s2 = b.size();
        int ind1 = 0, ind2 = 0;
        while (ind1 < s1 && ind2 < s2) {
            if (a.get(ind1).compareTo(b.get(ind2)) <= 0)
                c.add(a.get(ind1++));
            else
                c.add(b.get(ind2++));
            if (c.size()==10)
                break;
        }
        while (ind1 < a.size()) {
            if (c.size()==10)
                break;
            c.add(a.get(ind1++));
        }
        while (ind2 < b.size()) {
            if (c.size()==10)
                break;
            c.add(b.get(ind2++));
        }
        return c;
    }
    private static int nextInt() throws IOException{
        return Integer.parseInt(next());
    }
    private static double nextDouble() throws IOException{
        return Double.parseDouble(next());
    }
    private static long nextLong() throws IOException{
        return Long.parseLong(next());
    }
    private static String next() throws IOException {
        while (st == null || !st.hasMoreTokens()) {
            st = new StringTokenizer(in.readLine());
        }
        return st.nextToken();
    }
}